# Power Lab

 Materials: None Time Allotment: 3 Class Days

### Purpose:

The purpose of this lab is to perform measurements capable of determining the power rating of our own legs in lifting our bodies up a flight of stairs and to relate our understanding of power to the ability of other humans and machines to do work in a specified amount of time.

### Background:

All machines are typically described by a power rating. The power rating indicates the rate at which that machine can do work upon other objects. Thus, the power of a machine is the work/time ratio for that particular machine. To determine the power of a machine, one must be able to calculate the work done by the machine (through knowledge of the force it applies to displace an object) and the time it takes to do this amount of work.

A person is a machine which also has a power rating. Some people are more power-full than others; that is, they are capable of doing the same amount of work in less time. In this lab you will measure your own personal power by making measurements as you climb up a flight of stairs within your home. Additionally, you will perform one other activity in which you measure the power of your wrists, arms, etc.

### Analysis:

In order to accomplish the purpose of this lab, it would be useful to begin analyzing the physical situation which you will be investigating. Thus, before proceding with the measurements and calculations, answer the following questions.

1. In the space at the right, construct a free-body diagram showing all the forces acting upon your body as you climb up one flight of stairs at a constant speed. Label the forces according to type.

2. Discuss how you will be able to measure the upward force applied to your body as you climb the stairs at a constant speed. (HINT: 1 kg of mass on Earth is equivalent to 2.2 pounds of weight.)

3. Write two equations - one for the work done upon your body as you climb the stairs and one for the power generated by your body.

4. Make a list of all the quantities which need to be measured in order to determine your personal power as you elevate your body up a flight of stairs.

### Procedure:

Once you have established a good understanding of the measurements which need to be made, set up a data table, make measurements, and procede to calculate the power output of your body as you rapidly climb up a flight of stairs in your home. Use a ruler to determine the height of the stairs (Note: 12 in = 1 ft and 3.28 ft = 1.0 m). Use a stopwatch to determine the time.

### Data and Calculations:

Record all measured and known data below.

Calculate your power in the space below. PSYW

### Post-Lab Questions:

Express your understanding of the concept and mathematics of power by answering the following questions. Observe that some problems require you to determine the speed resulting from the power output of a person or machine. Consult the equation in your packet for such problems. Show all your work in an organized fashion.

1. A ski lift delivers two skiers to the top of a 500-meter tall hill every 12 s. The average mass of a skier plus equipment is 80 kg. Assuming dissipative forces are negligible, determine the power output of the chair lift motor.

2. A rock climber elevates her 55-kg body a height of 20 meters in 8 minutes. Determine her power output.

3. An elevator motor produces 2000 W. How fast (in m/s)can it lift a 1000-kg load?

4. The rate at which a man can do work is dependent upon a number of factors. It is found however, that there is a correlation between body mass and powet. In general, a man can do work at a rate of 8 Watts/kg during sustained activity. Given this value, how fast (in m/s) can he run up stairs?

5. A car must do work at a rate of 10 kW to maintain a constant speed of 25 m/s on flat ground. How large are the forces opposing its motion?

6. Engineers have contemplated the usefulness of harnessing the tides in the Bay of Fundy (in Canada) as a source of electrical power generation. Because of the shape of the bay, the difference between low and high tide can be as high as 17 meters; however, on average, the difference between low tide and high tide is 4 meters. The shape of the bay can be approximated as a rectangle with a width of 65 km and a length of 300 km.
1. Calculate the volume of water that flows out of the bay between high tide and low tide.

2. Given that the density of water is 1000 kg/m3, calculate the mass of this water.

3. Assuming that the mass calculated in part b is lowered a distance of 2.0 m over a time period of 6 hours, calculate the work which it is capable of delivering to an electrical generation device.

### Conclusion:

Write a conclusion which relates to the purpose of this lab.